Combine strawberries, lemon juice and sugar and toss to coat. Allow
strawberries to macerate at least 1 1/2 hours, until sugar is
dissolved.

Pour strawberries into a deep non-reactive sauté
pan and bring to a simmer over medium heat. Reduce heat to maintain
a gentle simmer, watching carefully to avoid burning on the bottom.

Cook, stirring occasionally, until juices are
thick and large bubbles form -- it should be dark red and look like
jam. Transfer jam to a heatproof bowl and allow to cool. While
strawberries cook, prepare ice cream base.

Combine milk and vanilla bean in a heavy saucepan and bring to a
boil. Remove from heat and allow to steep for 10 minutes. Whisk
together yolks and sugar until smooth. While whisking, add a small
amount of hot milk into yolk mixture to temper, then add remaining
milk and whisk until combined.

Return custard to saucepan and cook over low
heat, stirring constantly with a wooden spoon, until custard coats
the back of the spoon (about 170°F.).

Immediately strain custard and cream and chill
(on ice to speed things along). When custard and strawberries are
cool, whisk together until uniform.